Proposal of New Index for Describing Node Centralities Based on Oscillation Dynamics on Network

Takano

Murata

2018

IEICE Trans. Commun.

Self Cite

115

SUMMARYThis paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.

Section: Discussionmentioning

confidence: 99%

Section: Node Centrality and Oscillation Energymentioning

confidence: 99%

“…The oscillation energy can be defined even for damped oscillation on networks. Detailed discussion is presented in [16], [17].…”

Section: Node Centrality and Oscillation Energymentioning

confidence: 99%

“…The oscillation energy of each node gives a generalization of node centrality [16], [17]. To demonstrate the relationship, we use the network model shown in Fig.…”

Section: Node Centrality and Oscillation Energymentioning

confidence: 99%

See 2 more Smart Citations

Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction

Takano

Murata

2018

IEICE Trans. Commun.

Self Cite

115

“…Oscillation dynamics are quite different from the above topics. Recently, we introduced an oscillation model on networks and investigated its properties [9], [10], [11], [12], [13]. The significance of our oscillation model is that the oscillation energy of each node gives a generalized node centrality that describes the strength of the node's activity.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Model of Flaming Phenomena in On-Line Social Networks

Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017

Takano

Murata

2017

Self Cite

This paper proposes an oscillation model for describing the flaming phenomena in on-line social networks, and discusses countermeasures to flaming based on the proposed oscillation model. The most significant feature of the proposed model is that the cause of flaming can be explained by the structure of the network. Based on the proposed model, we can suppress the generation of flaming by controlling link weights of a part of the network. This passive solution to flaming is important for the stable operation of social media networks.

Derivation and characteristics of closed‐form solutions of the fundamental equations for online user dynamics

Ikeya

Concurrency and Computation

2021

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Summary The oscillation model, based on the wave equation on networks, can describe user dynamics in online social networks. The fundamental equation of user dynamics can be introduced into the oscillation model to explicitly describe the causal relation of user dynamics yielded by certain specific network structures. Moreover, by considering the sparseness of the link structure of online social networks, a novel fundamental equation of different forms has been devised. In this article, we derive a closed‐form solution of the new fundamental equation. Also, we show that the closed‐form solution of the new fundamental equation can generate the general solution of the original wave equation and investigate the characteristics of the derived general solution.